In a similar fashion the same parameter can be added to the "/rest/api/1.0/admin/users" request. For example:

<Bitbucket URL>/rest/api/1.0/admin/users?filter=admin&avatarSize=64

This parameter can be added to any request and the avatarUrl will be then added to the user details. For example, this is how you can request for the details of a pull request and include the avatarUrl:

We’ve been building a plugin to integrate Bitbucket Server and Jenkins CI, and I’m excited to announce that our alpha is ready to download and install. It lets you seamlessly configure a Jenkins job ...